University of TabrizComputational Methods for Differential Equations2345-39822383-25334420161001Solutions structure of integrable families of Riccati equations and their applications to the perturbed nonlinear fractional Schrodinger equation261275ENAhmadNeiramehGonbad Kavous Universitya.neirameh@gmail.comSaeidShokoohGonbad Kavous Universityshokooh.sd@gmail.comMostafaEslamiMazandaran Universitymostafaeslami1@gmail.comSome preliminaries about the integrable families of Riccati equations and solutions structure of these equations in several cases are presented in this paper, then by using of definitions for fractional derivative we apply the new extended of tanh method to the perturbed nonlinear fractional Schrodinger equation with the kerr law nonlinearity. Finally by using of this method and solutions of Riccati equations we obtain several analytical solutions for perturbed nonlinear fractional Schrodinger equation. The proposed technique enables a straightforward derivation of parameters of solitary solutions.Riccati equations,tanh method,Analytical solutionhttp://cmde.tabrizu.ac.ir/article_5643.htmlhttp://cmde.tabrizu.ac.ir/article_5643_67059c561d0c6654f169bd004b37123b.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39822383-25334420161001On asymptotic stability of Prabhakar fractional differential systems276284ENMohammadrezaAhmadi DaraniDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O. Box 115, Shahrekord, Iran.ahmadi.darani@sci.sku.ac.irMohammad HosseinDerakhshanDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O.Box 115, Shahrekord, Iranm.h.derakhshan.20@gmail.comAlirezaAnsariDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O.Box 115, Shahrekord, Iranalireza_1038@yahoo.comRezaKhoshsiarDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O.Box 115, Shahrekord, Irankhoshsiar@sci.sku.ac.irIn this article, we survey the asymptotic stability analysis of fractional differential systems with the Prabhakar fractional derivatives. We present the stability regions for these types of fractional differential systems. A brief comparison with the stability aspects of fractional differential systems in the sense of Riemann-Liouville fractional derivatives is also given. Asymptotically stable,Prabhakar fractional derivative,Generalized Mittag-Leffer function,Riemann-Liouville fractional derivativehttp://cmde.tabrizu.ac.ir/article_5645.htmlhttp://cmde.tabrizu.ac.ir/article_5645_de0b06fb29625a6c8d276eb9fc20e84a.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39822383-25334420161001Positive solutions for discrete fractional initial value problem285297ENTaherehHaghiSahand University of Technologytaherehhaghi@gmail.comKazemGhanbariSahand University of Technology, Irankghanbari@sut.ac.ir‎‎In this paper‎, ‎the existence and uniqueness of positive solutions for a class of nonlinear initial value problem for a finite fractional difference equation obtained by constructing the upper and lower control functions of nonlinear term without any monotone requirement‎ .‎The solutions of fractional difference equation are the size of tumor in model tumor growth described by the Gompertz function‎. ‎We use the method of upper and lower solutions and Schauder fixed point theorem to obtain the main results‎.discrete fractional calculus,existence of solutions,Positive solution‎, ‎Fixed point theoremhttp://cmde.tabrizu.ac.ir/article_5644.htmlhttp://cmde.tabrizu.ac.ir/article_5644_90f2bdba699867d7927f805399e1c7bf.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39822383-25334420161001Polynomial and non-polynomial solutions set for wave equation with using Lie point symmetries298308ENRezaHejaziShahrood university of technologyra.hejazi@gmail.comElhamLashkarianShahrood university of technologylashkarianelham@yahoo.com‎This paper obtains the exact solutions of the wave equation as a second-order partial differential equation (PDE)‎. ‎We are going to calculate polynomial and non-polynomial exact solutions by using Lie point symmetry‎. ‎We demonstrate the generation of such polynomial through the medium of the group theoretical properties of the equation‎. ‎A generalized procedure for polynomial solution is presented and this extended to the construction of related polynomials‎.Wave equation‎,‎Symmetry‎,‎Similarity solution‎http://cmde.tabrizu.ac.ir/article_5660.htmlhttp://cmde.tabrizu.ac.ir/article_5660_9ecafe6aa9271d65c1fe9c2008211643.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39822383-25334420161001Application of high-order spectral method for the time fractional mobile/immobile equation309322ENHosseinPourbashashDepartment of Mathematics, University of Garmsar, Garmsar-Iranh.pourbashash@ugsr.irIn this paper, a numerical eﬃcient method is proposed for the solution of time fractional mobile/immobile equation. The fractional derivative of equation is described in the Caputo sense. The proposed method is based on a ﬁnite difference scheme in time and Legendre spectral method in space. In this approach the time fractional derivative of mentioned equation is approximated by a scheme of order O(τ2−γ) for 0 < γ < 1. Also, we introduce the Legendre and shifted Legendre polynomials for full discretization. The aim of this paper is to show that the spectral method based on the egendre polynomial is also suitable for the treatment of the fractional partial differential equations. Numerical examples conﬁrm the high accuracy of proposed scheme. Time fractional,mobile/immobile (MIM) equation,finite difierence,spectral method,Legendre collocation methodhttp://cmde.tabrizu.ac.ir/article_5738.htmlhttp://cmde.tabrizu.ac.ir/article_5738_b83958c5c246fe0f1db8c9f6d51f6913.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39822383-25334420161001An efficient approximate method for solution of the heat equation using Laguerre-Gaussians radial functions323334ENMarziehKhaksarfardAlzahra Universitykhaksarfard.m@gmail.comYadollahOrdokhaniAlzahra Universityordokhani2000@yahoo.comEsmailBabolianKharazmi Universitybabolian@khu.ac.irIn the present paper, a numerical method is considered for solving one-dimensionalheat equation subject to both Neumann and Dirichlet initial boundaryconditions. This method is a combination of collocation method and radial basis functions (RBFs). The operational matrix of derivative for Laguerre-Gaussians (LG) radial basis functions is used to reduce the problem to a set of algebraic equations. The resultsof numerical experiments are presented to confirm the validity and applicabilityof the presented scheme.Radial basis functions,Heat conduction,Dirichlet and Neumann boundary Conditionshttp://cmde.tabrizu.ac.ir/article_5821.htmlhttp://cmde.tabrizu.ac.ir/article_5821_b2568988dc65b39325476c9da38f1f70.pdf